Step-by-step explanation:
Using similar triangles, the height and width of the water is proportional to the height and width of the trough.
w / h = 5 / 1
w = 5h
The volume of the water is:
V = AL
V = (½ wh) (14)
V = 7wh
Substituting:
V = 7(5h)h
V = 35h²
Take derivative with respect to time:
dV/dt = 70h dh/dt
Given that dV/dt = 15 and h = ⅓:
15 = 70 (⅓) dh/dt
dh/dt = 9/14
dh/dt ≈ 0.643 ft/min
Answer:
Step-by-step explanation:
The directrix given to us has equation,
and the focus is 
.
This means that the axis of symmetry of the parabola is parallel to the y-axis and has equation 
, because it must go through the focus.
This axis of symmetry of the parabola will meet the directrix at 
.
The vertex of this parabola is the midpoint of the point of intersection of the axis of symmetry and the focus.
Thus,
.
The equation is given by 
.
.
is the distance between the vertex and the focus, which is 2.
This implies that,
or 
But the position of the directrix and the vertex implies that the parabola opens downwards.
.
The equation of the parabola now becomes;
.
We solve for y to obtain,
or
The question being the case, the equation is: 8x + 6y = 136.
Where x is the number of hours spent on job A and y is the number of house spent on job B. Now to solve for both variables.
Notice that if you add x and y, you should get a total of 20 hours so x + y = 20.
To get x, x = 20 - y. Replace the answer on the original equation gives you 8(20-y) + 6y = 136.
160 - 8y + 6y = 136
160 - 2y = 136
-2y = 136 - 160
-2y = -24
<span>Solve for y by dividing both sides of this equation by -2 to get y:
y = 12
Replace y on the x + y = 20 equation to get x.
x + 12 = 20
x = 20 = 12
x = 8
Therefore:
x = 8 hours on job A
y = 12 hours on job B
Hope this helps!</span>
Answer:
LR is 12
Step-by-step explanation:
LP is hypotenuse and PR is base so LR is perpendicular
formula to calculate perpendicular is
p^2=H^2 -b^2
p^2=15^2-9^2
p^2=225-81
p^2=144
p=12(root of 144 is 12)
Answer:
axy under
Step-by-step explanation:
